Would it really cause problems if it did? I'm thinking if it got into the hotend (especially at the small amounts we're talking about), it would probably just melt into the molten filament and not really cause any issues.
There are "filament filters" that are for keeping foreign materials from getting into the hotend, but they're more for particulate things that won't melt and might clog the nozzle. Tape residue (again, at such small quanties) surely would just flow through with the molten filament and be unnoticeable in the final prints.
I'd definitely be more inclined to think tape could be more of a concern than jist the adhesive. Probably if it were me, I'd just try to be more thorough about removing all the tape from the spool (and not worry about small amounts of residual adhesive.)
Also, a description and/or picture of the filament and tape you're talking about could help.